Convergence Rates of Random Walk on Irreducible Representations of Finite Groups

Commutation Relations and Markov Chains

It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary distribution is the Ewens distribution, and some birth-death chains.

Separation Cutoffs for Random Walk on Irreducible Representations

Random walk on the irreducible representations of the symmetric and general linear groups is studied. A separation distance cutoff is proved and the exact separation distance asymptotics are determined. A key tool is a method for writing the multiplicities in the Kronecker tensor powers of a fixed representation as a sum of non-negative terms. Connections are made with the Lagrange-Sylvester in...

First Hitting times of Simple Random Walks on Graphs with Congestion Points

We derive the explicit formulas of the probability generating functions of the first hitting times of simple random walks on graphs with congestion points using group representations. 1. Introduction. Random walk on a graph is a Markov chain whose state space is the vertex set of the graph and whose transition from a given vertex to an adjacent vertex along an edge is defined according to some ...

On Finite Groups With Two Irreducible Character Degrees

Walks on Graphs and Lattices – Effective Bounds and Applications

A. We continue the investigations started in [7, 8]. We consider the following situation: G is a finite directedgraph,where to each vertex of G is assigned an element of a finite group Γ. We consider all walks of length N on G, starting from vi and ending at v j. To each such walk w we assign the element of Γ equal to the product of the elements along the walk. The set of all walks of le...